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Thermal and Entropy Analysis for a Lid-Driven Nanofluid Flow Under Inclined Magnetic Field and Radiation Effects

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Abstract

Energy-efficient thermal solutions necessitate investigation of nanofluid flows with entropy generation analysis, which reveals strategies to minimize irreversibilities and enhance efficiency of advanced systems such as electronic cooling, solar collectors, and nuclear reactors. Motivated by this, the study investigates the role magnetic field inclination and thermal radiation on free convection and entropy formation in a lid-driven nanofluid flow in square enclosure. The governing equations, for velocity field and temperature are coupled nonlinear partial differential equations. The solution ascertainment with the finite difference method includes “successive over-relaxation (SOR)” and “successive under-relaxation (SUR)” and Gauss–Seidel methods. The influences of pertinent parameters "Rayleigh number (104 ≤ Ra ≤ 106), Hartmann number (5 ≤ Ha ≤ 20), Radiation number (0 ≤ Rd ≤ 5), Reynolds number (20 ≤ Re ≤ 100), magnetic field inclination angles (0° ≤ Γ≤ 90°) and nanoparticle volume fraction (0 ≤ ϕ ≤ 0.04)” on flow and heat transportation are computed and analyzed through graphs. The findings reveal that the average Nusselt number upsurges with the rise of Ra and Rd, while decreases with Ha. The heat transfer rate intensifies as Rd increases; however, this rate falls when Ha rises. The entropy development is potentially high in the process of conductive heat transfer relative to the convective heat transfer. A major insight from this research is that augmenting the magnetic field inclination angle (Γ) markedly decreases entropy generation within the enclosure, indicating that precise orientation of the magnetic field offers an efficient control strategy to mitigate irreversibilities and enhance the thermal efficiency of thermal systems. The total entropy generation upsurge as Re, Ha, and Rd are increased on the other hand it diminishes when the amount of ϕ and Γ are increased.

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Data Availability

No datasets were generated or analysed during the current study.

Abbreviations

B0 :

Magnetic field strength

Beav :

Average Bejan number

Cp :

Specific heat at constant pressure

H:

Dimensional length & width scale of enclosure

Ha:

Hartmann number

k:

Thermal conductivity

Nuav :

Average Nusselt number

Nulocal :

Local Nusselt number

Pr:

Prandtl number

(p, P):

Dimensional & non-dimensional pressure

(T, \(\uptheta \)):

Dimensional & non-dimensional temperature

(u, v):

Dimensional velocities in ‘x & y’ directions

(U, V):

Non-dimensional velocities in ‘x & y’ directions

Ra:

Rayleigh number

Rd:

Radiation parameter

Re:

Reynolds number

SND, FF :

Local non-dimensional entropy formation due to fluid friction

SND, HT :

Local non-dimensional entropy formation due to heat transfer

SND, L :

Local non-dimensional total entropy formation

SND, MF :

Local non-dimensional entropy formation due to magnetic field

SND, T :

Total entropy formation

ST, HT :

Total entropy formation due to heat transfer

Uo :

Characteristic velocity

f:

Base fluid

nf:

Nanofluid

p:

Nanoparticle

\(\Gamma \) :

Magnetic field inclination angle

\(\upphi \) :

Nanoparticle volume fraction

\(\alpha \) :

Thermal diffusivity (\({\text{m}}^{2}{\text{s}}^{-1}\))

\(\beta \) :

Volumetric thermal expansion coefficient (\({\text{K}}^{-1}\))

\(\mu \) :

Dynamic viscosity

\(\nu \) :

Kinematic viscosity

\(\rho \) :

Density

\(\psi \) :

Stream function

\(\omega \) :

Vorticity

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Acknowledgements

Solomon Shiferaw is thankful to the Wolkite University, Ethiopia.

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Authors and Affiliations

  1. Department of Mathematics, Wolkite University, Wolkite, Ethiopia

    Solomon Shiferaw

  2. Department of Mathematics Organization, Guru Jambheshwar University of Science and Technology, Hisar, Haryana, 12001, India

    Solomon Shiferaw, Mukesh Kumar Sharma & Anil Ahlawat

  3. Department of Mathematics and Statistics, Manipal University Jaipur, Jaipur, Rajasthan, 303007, India

    Anil Ahlawat

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  1. Solomon Shiferaw
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  2. Mukesh Kumar Sharma
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Contributions

Author-1 did mathematical modeling of the proposed problem under the supervision of the corresponding author-2, and solved it numerically. The Matlab code was generated by author-1 and author-3. Computation of output was performed by authors 1 and 2. Text of the manuscript was written by author 2 with the guidance of the corresponding author. The outcomes were finalized collectively and presented in the result part.

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Correspondence to Mukesh Kumar Sharma.

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Shiferaw, S., Sharma, M. & Ahlawat, A. Thermal and Entropy Analysis for a Lid-Driven Nanofluid Flow Under Inclined Magnetic Field and Radiation Effects. Int. J. Appl. Comput. Math 12, 80 (2026). https://doi.org/10.1007/s40819-026-02147-1

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